Answer
$x=\frac{3}{2}~~$ or $~~x=-2$
Work Step by Step
Let's consider a trinomial in this form: $~ax^2+bx+c$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = a\times c$
Then the next step is to write the trinomial as follows:
$~x^2+bx+c = ax^2+rx+sx+c$
Let's consider this equation: $~2x^2+x-6 = 0$
To factor the left side of this equation, we need to find two numbers $r$ and $s$ such that $r+s = 1$ and $r\times s = -12$. We can see that $(4)+(-3) = 1~$ and $(4)\times (-3) = -12$
We can solve the equation as follows:
$2x^2+x-6 = 0$
$2x^2+4x-3x-6 = 0$
$(2x^2+4x)+(-3x-6) = 0$
$(2x)(x+2)+(-3)(x+2) = 0$
$(2x-3)~(x+2) = 0$
$2x-3 = 0~~$ or $~~x+2 = 0$
$x=\frac{3}{2}~~$ or $~~x=-2$
